Alison Smith, one of the alleged victims, said on Twitter: "The linen needs to be washed one way or another, especially when the threat to women is ongoing."

In comments to reporters, Mr Carmichael said that the peer "should apologise".

He said: "I think that it is not good for any political party to be seen to be washing its dirty linen in public. Sadly it is happening here."

Asked how he would characterise the "situation", he said: "I would say scandal without the sex."

He added: "We are in a situation where you have effectively got two camps and at a time when you are seeing the economy turning a corner, economic growth taking hold, I think there is a frustration amongst the party activists that we are not able to talk about that because we are talking so much about our own internal matters.

“What I am quite keen to see is that there is a some sort of mediation set up that will allow both parties to find a way through this because clearly we have got something that now needs an early resolution and the only way I see achieving that is to have some third party involvement in mediation.”

He said mediation could be from a professional in the field or a party grandee but had to be “somebody trusted by both sides.”